These exercises demonstrate the content of the ByTheMark service. These are meant for private individuals for learning data structures and algorithms. If you want to try out more content, you can register to the ByTheMark Personal free of charge.

Search the k'th smallest element by the following algorithm. First, insert the given keys (Stream of Keys) one by one into the Heap below. Second, delete k=3 times the smallest element from the heaps. After each operation, make sure that the heap-order property: "the parent is smaller than its child" is preserved.

Insert a key by drag and dropping it into an empty node of the heap. Restore the heap order property after each insertion. Delete a key by clicking its node (not the key) and pressing the "Delete" button. Note, however, that drag and drop will swap the source and destination keys with each other. Thus, you can either delete the root node and swap the last element into the top of the tree or make the swap first and delete the last key. In both cases, the size of the heap is decremented.